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Comparison of doubling the size of image algorithms
Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 4, pp. 389-400 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this paper the comparative analysis for quality of some interpolation non-adaptive methods of doubling the image size is carried out. We used the value of a mean square error for estimation accuracy (quality) approximation. Artifacts (aliasing, Gibbs effect (ringing), blurring, etc.) introduced by interpolation methods were not considered. The description of the doubling interpolation upscale algorithms are presented, such as: the nearest neighbor method, linear and cubic interpolation, Lanczos convolution interpolation (with $a=1, 2, 3$), and $17$-point interpolation method. For each method of upscaling to twice optimal coefficients of kernel convolutions for different down-scale to twice algorithms were found. Various methods for reducing the image size by half were considered the mean value over $4$ nearest points and the weighted value of $16$ nearest points with optimal coefficients. The optimal weights were calculated for each method of doubling described in this paper. The optimal weights were chosen in such a way as to minimize the value of mean square error between the accurate value and the found approximation. A simple method performing correction for approximation of any algorithm of doubling size is offered. The proposed correction method shows good results for simple interpolation algorithms. However, these improvements are insignificant for complex algorithms ($17$-point interpolation, Lanczos $a=3$). According to the results of numerical experiments, the most accurate among the reviewed algorithms is the $17$-point interpolation method, slightly worse is Lanczos convolution interpolation with the parameter $a=3$ (see the table at the end).
Mots-clés : interpolation, 17-point interpolation.
Keywords: convolution of function, Lanczos filter 
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S. E. Vaganov; S. I. Khashin. Comparison of doubling the size of image algorithms. Modelirovanie i analiz informacionnyh sistem, Tome 23 (2016) no. 4, pp. 389-400. http://geodesic.mathdoc.fr/item/MAIS_2016_23_4_a0/

[1] Vatolin D. et al., Metody szhatiya dannykh. Ustroystvo arkhivatorov, szhatie izobrazheniy i video, Dialog – MIFI, M., 2002, 384 pp. (in Russian)

[2] Gonsales R., Vuds R., Tsifrovaya obrabotka izobrazheniy, Tekhnosfera, M., 2012, 1104 pp. (in Russian)

[3] Prett U., Tsifrovaya obrabotka izobrazheniy, v. 1, Mir, M., 1982, 312 pp. (in Russian)

[4] Khashin S. I., “Semnadtsatitochechnaya interpolyatsionnaya formula ot 2 peremennykh”, Ivanovo State University Bulletin, 2003, no. 3, 133–137 (in Russian)

[5] Yane B., Tsifrovaya obrabotka izobrazheniy, Tekhnosfera, M., 2007, 583 pp. (in Russian)

[6] Burger W., Burge M. J., Principles of digital image processing: core algorithms, Springer-Verlag, London, 2009, 327 pp. | Zbl

[7] Taubman D. S., Marcellin M. V., JPEG2000: image compression fundamentals, standards, and practice, Springer Science+Business Media, LLC, 2002, 773 pp.

[8] Wallace G. K., “The JPEG still picture compression standard”, IEEE Transactions on Consumer Electronics, 38:1 (1992), xviii–xxxiv | DOI

[9] Keys R. G., “Cubic Convolution Interpolation for Digital Image”, Processing IEEE transaction on acoustics, speech, and signal processing, 29:6 (1981), 1153–1160 | DOI | MR | Zbl

[10] Klette R., Concise Computer Vision. An Introduction into Theory and Algorithms, Springer-Verlag, London, 2014, 429 pp. | Zbl

[11] Li X., Orchard M. T., “New Edge-Directed Interpolation”, IEEE Transactions on Image Processing, 10:10 (2001), 1521–1527 | DOI | MR